Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.00452

Single-site dissipation stabilizes a superconducting nonequilibrium steady state in a strongly correlated system

X. Z. Zhang

quant-phcond-mat.str-elSubmitted Jan 31, 2026• Announced Feb 3, 2026• 0 citations• Revised Feb 5, 2026 (v2)
v1 · Jan 31, 2026v2 · Feb 5, 2026
arXivHTMLPDF

Abstract

Can superconducting order be engineered as a robust attractor of open-system dynamics in strongly correlated systems? We demonstrate this possibility by proposing a minimal dissipation-engineering protocol for the particle-hole symmetric Hubbard model. By applying a rotated quantum jump operator, specifically a locally transformed $η$-pair lowering operator, on a single lattice site only, we show that the Lindblad evolution autonomously pumps the system from the vacuum into a nonequilibrium steady state (NESS) exhibiting macroscopic $η$-pair off-diagonal long-range order (ODLRO). Crucially, this local-to-global synchronization stands in stark contrast to schemes reliant on spatially extensive reservoirs: here, a single local dissipative seed suffices to establish long-range coherence across the entire interacting lattice system. We elucidate the underlying mechanism via three core features: local dark-state selection, the controlled elimination of off-manifold excursions induced by hopping, and a Liouvillian invariant-subspace structure that yields an attractive fixed point with a finite dissipative gap. Furthermore, we systematically classify the stability of this NESS with respect to static disorder, and identify a wide regime in which the superconducting attractor remains robust against Hamiltonian perturbations that preserve the effective subspace structure. We also pinpoint specific perturbations that directly cause dephasing of the $% η$-pseudospin coherence and suppress ODLRO. These findings open up a disorder-tolerant pathway for stabilizing superconducting order as a non-thermal attractor through minimal local quantum-jump control.

Comments
15 pages, 11 figures

Related papers

Dynamical preparation of a steady off-diagonal long-range order state in the Hubbard model with a local non-Hermitian impurity

X. Z. Zhang, Z. Song

The cooperation between non-Hermiticity and interaction brings about a lot of counterintuitive behaviors, which are impossible to exist in the framework of the Hermitian system. We study the effect of a non-Hermitian impurity on the Hubbard model in the context of $\ensuremath{\eta}$ symmetry. We show that the non-Hermitian Hubbard Hamiltonian can respect a full real spectrum even if a local non-Hermitian impurity is applied to. The balance between dissipation of single fermion and on-site pair fluctuation results in a highest-order coalescing state with off-diagonal long-range order (ODLRO). Based on the characteristic of high-order EP, the critical non-Hermitian Hubbard model allows the generation of such a steady superconducting-like state through the time evolution from an arbitrary initial state, including the vacuum state. Remarkably, this dynamic scheme is insensitive to the on-site interaction and entirely independent of the locations of particle dissipation and pair fluctuation. Our results lay the groundwork for the dynamical generation of a steady ODLRO state through the critical non-Hermitian strongly correlated system.

arXiv:2009.06167•Physical review. B./Physical review. B•Nov 6, 2020•18 citations

Dissipation-tunable extended and localized steady states in a non-disordered lattice

Ming-Jie Tao, Yi-Ting Wang, Jing Li +3 more

Dissipation is usually regarded as a source of decoherence that suppresses quantum interference and localization. Here we show that suitably engineered dissipation can instead be used to select localized or extended states in a strictly non-disordered one-dimensional lattice. The underlying clean lattice has spatially inhomogeneous hopping and supports both extended bulk states and localized boundary states, including an algebraically localized bound state in the continuum. We introduce a nonlocal bond jump operator with a tunable relative phase and show that this phase selectively favors eigenstates with different spatial phase correlations. As a result, the long-time density matrix can be steered toward sectors dominated by localized or extended Hamiltonian eigenstates without changing any Hamiltonian parameter. The microscopic origin of the selection is quantified by the fraction of site pairs separated by a distance $l$ that are phase matched with the dissipative channel. We further characterize the dissipative quench through the quantum fidelity and show that the selected character of the steady state can persist after the dissipation is removed. Our results establish phase-selective bond dissipation as a route to controllable state preparation and transport manipulation in non-disordered lattices.

quant-pharXiv:2608.19694•Aug 21, 2026•0 citations

Magnetization in a nonequilibrium quantum spin system

X. Z. Zhang

The dynamics described by the non-Hermitian Hamiltonian typically capture the short-term behavior of open quantum systems before quantum jumps occur. In contrast, the long-term dynamics, characterized by the Lindblad master equation, drive the system towards a nonequilibrium steady state (NESS), which is an eigenstate with zero energy of the Liouvillian superoperator, denoted as $\mathcal{L}$. Conventionally, these two types of evolutions exhibit distinct dynamical behaviors. However, in this study we challenge this common belief and demonstrate that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The criticality of the system arises from the exceptional point of the effective non-Hermitian Hamiltonian. Additionally, the NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. We apply this finding to a series of critical open quantum systems and show that a local dissipation channel can induce collective alignment of all spins in the same direction. This direction can be well controlled by modulating the quantum jump operator. The corresponding NESS is a product state and maintains long-time coherence, facilitating quantum control in open many-body systems. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.

arXiv:2406.00268•Physical review. B./Physical review. B•May 31, 2024•4 citations

Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems

Orazio Scarlatella, Aashish A. Clerk, Rosario Fazio +1 more

A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.

•Jul 22, 2021•27 citations

Quantum synchronisation enabled by dynamical symmetries and dissipation

Joseph Tindall, Carlos Sánchez Muñoz, Berislav Buča +1 more

Abstract In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry—an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit long-lived signatures of both phase and frequency-locking.

arXiv:1907.12837•New Journal of Physics•Dec 12, 2019•90 citations

Entangling Superconducting Qubits via Energy-Selective Local Reservoirs

Qihao Guo, Botao Du, Ruichao Ma

Engineered dissipation provides a powerful route to controlling and stabilizing quantum states in open systems. Superconducting circuits are particularly suited to this approach due to their tunable coupling to dissipative environments. Here we realize programmable local reservoirs for superconducting qubits through parametrically driven coupling to readout resonators, creating energy-selective incoherent pump and loss. Using coupled superconducting qubits, we autonomously stabilize entangled single-excitation states with fidelity up to 90.8%. We probe the stabilization dynamics under varying initial conditions and bath parameters, and implement robust classical shadow estimation for accurate and scalable state characterization. Finally, we numerically study a configuration where the engineered pump and loss share a common dissipative mode, leading to reservoir-mediated interference and classically correlated steady states. Our results demonstrate a scalable and hardware-efficient framework for dissipative preparation and control of correlated many-body states in superconducting circuits.

quant-pharXiv:2605.12429•Physical Review Research•May 13, 2026•0 citations
Can superconducting order be engineered as a robust attractor of open-system dynamics in strongly correlated systems? We demonstrate this possibility by proposing a minimal dissipation-engineering protocol for the particle-hole symmetric Hubbard model. By applying a rotated quantum jump operator, specifically a locally transformed ηηη-pair lowering operator, on a single lattice site only, we show that the Lindblad evolution autonomously pumps the system from the vacuum into a nonequilibrium steady state (NESS) exhibiting macroscopic ηηη-pair off-diagonal long-range order (ODLRO). Crucially, this local-to-global synchronization stands in stark contrast to schemes reliant on spatially extensive reservoirs: here, a single local dissipative seed suffices to establish long-range coherence across the entire interacting lattice system. We elucidate the underlying mechanism via three core features: local dark-state selection, the controlled elimination of off-manifold excursions induced by hopping, and a Liouvillian invariant-subspace structure that yields an attractive fixed point with a finite dissipative gap. Furthermore, we systematically classify the stability of this NESS with respect to static disorder, and identify a wide regime in which the superconducting attractor remains robust against Hamiltonian perturbations that preserve the effective subspace structure. We also pinpoint specific perturbations that directly cause dephasing of the % η-pseudospin coherence and suppress ODLRO. These findings open up a disorder-tolerant pathway for stabilizing superconducting order as a non-thermal attractor through minimal local quantum-jump control.
The cooperation between non-Hermiticity and interaction brings about a lot of counterintuitive behaviors, which are impossible to exist in the framework of the Hermitian system. We study the effect of a non-Hermitian impurity on the Hubbard model in the context of $\ensuremath{\eta}$ symmetry. We show that the non-Hermitian Hubbard Hamiltonian can respect a full real spectrum even if a local non-Hermitian impurity is applied to. The balance between dissipation of single fermion and on-site pair fluctuation results in a highest-order coalescing state with off-diagonal long-range order (ODLRO). Based on the characteristic of high-order EP, the critical non-Hermitian Hubbard model allows the generation of such a steady superconducting-like state through the time evolution from an arbitrary initial state, including the vacuum state. Remarkably, this dynamic scheme is insensitive to the on-site interaction and entirely independent of the locations of particle dissipation and pair fluctuation. Our results lay the groundwork for the dynamical generation of a steady ODLRO state through the critical non-Hermitian strongly correlated system.
Dissipation is usually regarded as a source of decoherence that suppresses quantum interference and localization. Here we show that suitably engineered dissipation can instead be used to select localized or extended states in a strictly non-disordered one-dimensional lattice. The underlying clean lattice has spatially inhomogeneous hopping and supports both extended bulk states and localized boundary states, including an algebraically localized bound state in the continuum. We introduce a nonlocal bond jump operator with a tunable relative phase and show that this phase selectively favors eigenstates with different spatial phase correlations. As a result, the long-time density matrix can be steered toward sectors dominated by localized or extended Hamiltonian eigenstates without changing any Hamiltonian parameter. The microscopic origin of the selection is quantified by the fraction of site pairs separated by a distance lll that are phase matched with the dissipative channel. We further characterize the dissipative quench through the quantum fidelity and show that the selected character of the steady state can persist after the dissipation is removed. Our results establish phase-selective bond dissipation as a route to controllable state preparation and transport manipulation in non-disordered lattices.
The dynamics described by the non-Hermitian Hamiltonian typically capture the short-term behavior of open quantum systems before quantum jumps occur. In contrast, the long-term dynamics, characterized by the Lindblad master equation, drive the system towards a nonequilibrium steady state (NESS), which is an eigenstate with zero energy of the Liouvillian superoperator, denoted as L\mathcal{L}L. Conventionally, these two types of evolutions exhibit distinct dynamical behaviors. However, in this study we challenge this common belief and demonstrate that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The criticality of the system arises from the exceptional point of the effective non-Hermitian Hamiltonian. Additionally, the NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. We apply this finding to a series of critical open quantum systems and show that a local dissipation channel can induce collective alignment of all spins in the same direction. This direction can be well controlled by modulating the quantum jump operator. The corresponding NESS is a product state and maintains long-time coherence, facilitating quantum control in open many-body systems. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.
A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.
Abstract In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry—an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit long-lived signatures of both phase and frequency-locking.
Engineered dissipation provides a powerful route to controlling and stabilizing quantum states in open systems. Superconducting circuits are particularly suited to this approach due to their tunable coupling to dissipative environments. Here we realize programmable local reservoirs for superconducting qubits through parametrically driven coupling to readout resonators, creating energy-selective incoherent pump and loss. Using coupled superconducting qubits, we autonomously stabilize entangled single-excitation states with fidelity up to 90.8%. We probe the stabilization dynamics under varying initial conditions and bath parameters, and implement robust classical shadow estimation for accurate and scalable state characterization. Finally, we numerically study a configuration where the engineered pump and loss share a common dissipative mode, leading to reservoir-mediated interference and classically correlated steady states. Our results demonstrate a scalable and hardware-efficient framework for dissipative preparation and control of correlated many-body states in superconducting circuits.